PLOT FUNCTION

be6cd773-cd33-49e4-a833-50d2f792c2e5 14 4 5 true true 0 decimal

&[DATE] &[TIME] - &[FILENAME]

PLOT FUNCTION

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

THIELE COEFFICIENTS

Data Yfit Thiele_Coeffs X Data 1 col : Y Data 2 col : n Data rows : 13 mat j 1 n range j 1 ≡ i 1 n range Table i j el Y i el : for f j 1 - : i j n range Table i j el X f el X i el - Table f f el Table i j 1 - el - / : Cont j : 21 line break try for 21 line if 11 line for i 1 Cont range Yφ i el Table i i el 4 round : for Yfit Yφ : 41 line :

THIELE FUNCTION

s P p size T i size 2 range i size ≡ T s i 1 - el eval p P i 1 - el eval - s i el eval / (+ : T T : 21 line T s i 1 - el eval p P i 1 - el eval - T / (+ : T T : 21 line if for s P p size T T : 21 line :

CHOLESKY FUNCTION

Order Data CholeskyF i 1 Order 1 + (range i 1 ≡ φ i el 1 : φ i el x i 1 -^: if for x φ φ : k2 x φ length : X Data 1 col : n X length : Y Data 2 col : 14 mat j 1 k2 range i 1 n range Xi i j el X i el φ j el : for for M1 Xi transpose Xi * : M2 Xi transpose Y * : 12 mat B1 M1 1 -^eval M2 * : i 1 Order 1 + (range i 1 ≡ R B1 i el eval : R R B1 i el x i 1 -^* + : if for R 81 line :

LEAST SQUARES FUNCTION

T X Y Order f T 1 ≡ m Order 1 + : m 2 : if n X rows : 12 mat i 1 m range j 1 m range con i 1 - (j 1 - (+ : i 1 ≡ (j 1 ≡ (& A i j el n : 11 line T 1 ≡ (T 2 ≡ (| A i j el X k el (con^k 1 n sum : A i j el X k el ln (con^k 1 n sum : if if 21 line for for i 1 m range i 1 ≡ B i el Y k el k 1 n sum : B i el X k el (i 1 -^Y k el * k 1 n sum : if T 1 ≡ i 1 ≡ B i el Y k el ln k 1 n sum : B i el X k el (Y k el ln * k 1 n sum : if T 2 ≡ i 1 ≡ B i el Y k el ln k 1 n sum : B i el X k el ln Y k el ln * k 1 n sum : if cases for i 1 m range φ i el 1 : i 1 ≡ φ i el x (i 1 -^: cases for T 1 ≡ φ 1 el x : 11 line T 2 ≡ (T 3 ≡ (| cases β A 1 -^B * : ff 0 : i 1 m range ff ff β i el φ i el * + : for ff 31 line T 1 ≡ ff β 1 el exp β 2 el φ 1 el * exp * : T 2 ≡ ff β 1 el exp φ 1 el (β 2 el^* : T 3 ≡ cases ff 71 line :

1. Enter a set of measured data representing the saturation temperature of boiling water in °C.

Data 0.1 45.8 0.5 81.32 1 99.61 2.5 127.41 5 151.84 10 179.89 25 223.96 50 263.94 100311150 342.16 200 365.75 220 373.71 122 mat :

P Data 1 col :

T Data 2 col :

PRESSURE; BAR P 0.1000 0.5000 1.000 2.500 5.000 10.00 25.00 50.00 100.0 150.0 200.0 220.0 121 mat

TEMPERATURE, °C T 45.80 81.32 99.61 127.4 151.8 179.9 224.0 263.9 311.0 342.2 365.8 373.7 121 mat

2. Use the Thiele method to interpolate a curve through the data set.

THIELE COEFFICIENTS β Data Yfit Thiele_Coeffs :

β 45.80 0.01130 91.50 0.08020 92.00 0.2997 119.3 1.044 161.4 3.552 76.29 2.674 - 121 mat

THIELE FIT x TF β P x β rows T :

THIELE FUNCTION β P x β rows T 45.8 x 0.1 - 0.0113 x 0.5 - 91.5038 x 1 - 0.0802 x 2.5 - 92.001 x 5 - 0.2997 x 10 - 119.2705 x 25 - 1.044 x 50 - 161.3981 x 100 - 3.5519 x 150 - 76.2884 x 200 - 2.6735 - / + / + / + / + / + / + / + / + / + / + / +

3. Use the polynomial regression method to interpolate a curve through the data set.

CHOLESKY FIT (CUBIC) x CF 3 Data CholeskyF :

x CF 97.6219417280701 87151690693471638400000000 / x 21 -^* + 13291214623781335544320000000 / - (x 31 -^* + 5422368273289 5.36870912 1016^* / x 41 -^* +

LEAST SQUARE FIT x LSF 1 P T 6 f :

x LSF 739805568193264097541528685961 / 218937365609185001522538060526790 / x 21 -^* + 8516711169736711864274617482380 / - (x 31 -^* + 792809490520065112981165594537000 / x 41 -^* + 158969168478618029980053090222500000 / - (x 51 -^* + 424868426364519022116157757323000000000 / x 61 -^* + 4526830017781751695857912559230000000000 / - (x 71 -^* +

PT P T . 10 black plotG :

PT x TF x 0 > ( x 220 ≤ ( & cases x CF x 0 > ( x 220 ≤ ( & cases x LSF x 0 > ( x 220 ≤ ( & cases 4 1 sys

5. Compare the calculated results returned by the Thiele method to two mid-points from the steam tables.

75 TF 290.504

A 290.504 °C * :

A 563.654 K *

125 TF 327.782

B 327.782 °C * :

B 600.932 K *

mid-points calculated 290.52 °C * 75 TF bar * 327.78 °C * 125 TF bar * 32 mat mid-points calculated 563.67 K * 563.654 K * 600.93 K * 600.932 K * 32 mat ≡

The calculated data points match the published data very closely.

6. Using the Thiele interpolated curve, calculate the temperature at which water boils in Mexico city 2250m above sea level.

p_mexico 0.771 :

bar

p_mexico TF 92.39

°C